Double modulation experiments

If both the light intensity and the electrode potential are modulated at different frequencies, information may, in principle, be obtained at the sum and difference frequencies. This method has been little used the complexities of the a.c. impedance analysis in the light have precluded all but 

Inserting these expressions into eqn. (604) and using small-signal theory, we 

The advantage of this technique is that absolute photocurrent measurements are not needed both a and Lp result from the same experiment. This technique has been tried for p-GaP in 0.1 M EuC13/1 M HC104 and the results, at least at potentials well removed from Vr, and for low light intensities, are in reasonable accord with the above analysis as shown in Figs. 102 and 103. The values of a and Lp derived from these data lie within the range of values quoted in the literature. 

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There are other advantages of microelectrodes as compared to the macroelectrodes. Because the current is small, on the order of nA to pA, the voltage drop due to the electrical resistance of the medium is negligible. For this reason, it is possible to perform electrochemical experiments in media that would be otherwise unsuitable for macroelectrodes, such as resistive hydrocarbon solvents and solid electrolytes, without a potentiostat. Secondly, the double-layer capacitance is very small because the area of the electrode is small. This means that very fast modulation experiments... 

The nuclear Overhauser effect (NOE) is a consequence of the modulation of the dipole-dipole interactions (through space) between different nuclei and is correlated with the inverse sixth power of the internuclear distance. Experimentally, the NOE is the fractional change in intensity of one resonance when another resonance is irradiated in a double-irradiation experiment. The NOE phenomenon is intimately related to spin relaxation. The NOE varies as a function of the product of the Larmor frequency, co0, and the rotational correlation time, tc. In small molecules, tc is short relative to uo"1. In this extreme motional narrowing situation, the frequency... 

The overall spectrum showed no recognisable pattern and without further experimental evidence, assignment would have been difficult, if not impossible. Fortunately two other diagnostic studies of each resonance line could be made. It was possible to carry out double resonance experiments, using two different microwave frequencies simultaneously. Suppose that two resonance lines with frequencies f] and f2 have been observed. If they share a common energy level, a modulation signal on f2 may be... 

The development of the double resonance experiments described in Section 3.8.2 was targeted at spin- /i systems. TRAPDOR and Rotational-Echo Adiabatic Passage Double Resonance (REAPDOR) experiments are designed specifically for quadrupolar nuclei and do not work on systems containing only spin- /2 nuclei. These MAS experiments still rely on the modulation of the heteronuclear dipolar coupling (as in the REDOR experiment) to prevent an echo from refocusing, but the modulation is no longer by 180° pulses. 

In a similar experiment Frenkel et at " investigated CHjCP and and measured the influence of P(26) CO2 laser radiation on the microwave absorption. As was also reported in the earlier experiments, e.g., by Ronn and Lide, and by Shimizu and Oka, Frenkel and co-workers observed that in such a double resonance experiment not only the participating levels but also other rotational levels, vibrational levels, and even species of different isotopic composition are affected via collisional transfer. Frenkel et al also determined relaxation times. This was accomplished by modulating the laser intensity with a chopper whose speed could be varied between 80 and 4000 Hz and by measuring the rise time of the double resonance signal from which vibrational relaxation rates can be deduced. 

Not all the information can be obtained by the basic CW experiment that is considered by many chemists as all there is to EPR. Elucidating geometric structure or small spin densities requires the separation of small hyperfine couplings or dipole-dipole couplings between electron spins from larger interactions. This can be achieved by double resonance experiments, such as electron nuclear double resonance (ENDOR) [8,9] and electron electron double resonance (ELDOR) spectroscopy and further pulse-EPR techniques [10] such as electron spin echo envelope modulation (ESEEM). Pulse-EPR techniques may also provide more information on dynamic processes than simple CW experiments and may access longer time scales. 

Let us consider a double-modulation FT-IR spectrometry experiment in which a target sample and a reference sample are effectively placed between an infrared source and an interferometer, and the infrared beam from the source irradiates the target and reference samples alternately with a modulation frequency of/. The single-beam spectra of the target and reference samples may be denoted, respectively, by B (v) and 5 (5). As the infrared beam which has passed through the target and reference samples has been modulated with frequency / , its spectmm B v, t), a function of time t, is expressed in the following form. 

Table 17.15 shows results obtained from the application of various bulk and surface analysis methods to lithium metal at rest or after cyclization experiments, as well as at noble metal and carbon electrodes after cathodic polarization. Several surface and elemental analysis methods are applied, including X-ray photoelectron spectroscopy (XPS, ESCA/XPS), energy dispersive analysis of X-rays (X-ray microanalysis, EDAX), Eourier transform infrared spectroscopy (ETIR), Auger electron spectroscopy (AES), ellipsometry (E), electro-modulated infrared reflectance spectroscopy (EMIRS), double modulation Fourier transform infrared spectroscopy (DMFTIR), subtractively normalized interfacial Fourier transform infrared spectroscopy (SNIFTIRS), gas chromatography (GC), IR spectroscopy. X-ray diffraction (XRD), and atomic force microscopy (AFM). 

Quantum mechanically the modulation of the fluorescent light is associated with the radio frequency coherence of the excited state density matrix. In a standard Brossel-Bitter double-resonance experiment Tt-polarized light excites the atoms initially to the m=0 state of the excited level. Fig. 16.13(b), and then interaction with the r.f. magnetic field transforms each atom into a coherent superposition of the m=0, l states. The relative phases of the probability amplitudes of these states are fixed by the phase of the r.f. field and are the same for every atom of the sample. Thus the r.f. field is able to generate substantial hertzian coherence in the excited state density matrix. The fluorescent light emitted in the direction of B is then a coherent... 

Experimental investigation of modulation phenomena. Experiments which confirmed that the fluorescent light in a double-resonance experiment was strongly modulated were first reported by Dodd et aZ.(1959), but a more detailed account of the techniques employed is given in a later publication (Dodd et a7.1963). When the atoms were initially excited to a pure Zeeman state the intensity of the fluorescent light emitted in an arbitrary direction was found to be modulated at the frequencies Wq and 2<0q ... 

OPTICAL DOUBLE-RESONANCE EXPERIMENTS Modulation amplitude, D Modulation amplitude, E... 

Fig.16.14. Resonances in the amplitude o modulation o fluorescent light in an optical double-resonance experiment for the case u < r.

We have seen that in an optical double-resonance experiment the intensity of the fluorescent light is modulated at harmonics of the driving angular frequency Wq. The nutation which occurs at the angular frequency... 

Fig.16.15. Resonances observed at nutational frequencies in optical double-resonance experiments on atoms excited by intensity-modulated light. The upper part of the figure shows a plot of the relevant energy levels in the rotating coordinate system.

Recent work in our laboratory has shown that Fourier Transform Infrared Reflection Absorption Spectroscopy (FT-IRRAS) can be used routinely to measure vibrational spectra of a monolayer on a low area metal surface. To achieve sensitivity and resolution, a pseudo-double beam, polarization modulation technique was integrated into the FT-IR experiment. We have shown applicability of FT-IRRAS to spectral measurements of surface adsorbates in the presence of a surrounding infrared absorbing gas or liquid as well as measurements in the UHV. We now show progress toward situ measurement of thermal and hydration induced conformational changes of adsorbate structure. The design of the cell and some preliminary measurements will be discussed. 

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